Problem: Ashley is 3 times as old as Jessica. Four years ago, Ashley was 5 times as old as Jessica. How old is Jessica now?
Explanation: We can use the given information to write down two equations that describe the ages of Ashley and Jessica. Let Ashley's current age be $a$ and Jessica's current age be $j$ The information in the first sentence can be expressed in the following equation: $a = 3j$ Four years ago, Ashley was $a - 4$ years old, and Jessica was $j - 4$ years old. The information in the second sentence can be expressed in the following equation: $a - 4 = 5(j - 4)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $j$ , it might be easiest to use our first equation for $a$ and substitute it into our second equation. Our first equation is: $a = 3j$ . Substituting this into our second equation, we get: $3j$ $-$ $4 = 5(j - 4)$ which combines the information about $j$ from both of our original equations. Simplifying the right side of this equation, we get: $3 j - 4 = 5 j - 20$ Solving for $j$ , we get: $2 j = 16.$ $j = 8$.